Search Results

This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to population ecology. The mathematical sections start by constructing an individual-based model in homogeneous space, and then simplifies the model to derive the classical model of logistic population growth. The models are then expanded to heterogeneous space in two contrasting ways, resulting in models called the plant population model and the butterfly metapopulation model. Both types of models are used to analyse the consequences of habitat loss and fragmentation at the population level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of time-series data, species distribution modelling, and metapopulation modelling.

This chapter introduces mathematical and statistical modelling approaches in community ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to community ecology. The mathematical sections start with models of two interacting species in homogeneous space, including a model with competitive interactions, a resource–consumer model, and a predator–prey model. The competition model is expanded to heterogeneous space and to the case of many competing species. This model is used to analyse the consequences of habitat loss and fragmentation at the community level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on time-series data of two interacting species, point pattern analyses, and joint species distribution models.

This chapter introduces mathematical and statistical modelling approaches to study the ecology of movement. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to movement ecology. The mathematical sections first introduce random walk and diffusion models in homogeneous space, and use these models to illustrate the relationship between the Lagrangian and the Eulerian viewpoints. The movement models are then expanded to heterogeneous space, and in particular to highly fragmented patch networks. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of tracking data and capture-mark-recapture data.